Evaluation of certain families of log-cosine integrals using hypergeometric function approach and applications

Mohammad Idris Qureshi and Shakir Hussain Malik
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 499–515
DOI: 10.7546/nntdm.2024.30.3.499-515
Full paper (PDF, 288 Kb)

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Authors and affiliations

Mohammad Idris Qureshi
Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University)
New Delhi, 110025, India

Shakir Hussain Malik
Department of Mathematics, Government Degree College
Magam Budgam, Jammu and Kashmir, 193401, India

Abstract

In this paper, we provide the analytical solutions of the families of certain definite integrals: and in terms of multiple hypergeometric functions of Kampé de Fériet having the arguments and Riemann zeta functions. As applications, we obtain some mixed summation formulas (19), (35) and (46) involving generalized hypergeometric functions and having the arguments and other (possibly) new summation formulas (38) and (40) for multiple hypergeometric functions of Kampé de Fériet having the arguments also mixed relations (36) and (47) involving Riemann zeta functions.

Keywords

• Hypergeometric functions
• Log-cosine integrals
• Riemann zeta function
• Kampé de Fériet multiple hypergeometric functions

2020 Mathematics Subject Classification

• 33C05
• 33C20
• 11B65
• 11M06
• 33B20

References

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Manuscript history

• Received: 30 May 2023
• Revised: 3 June 2024
• Accepted: 19 September 2024
• Online First: 26 September 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).